Find the Absolute Extrema Of $f ( x , y ) = 4 x ^ { 2 } + 8 x y - 48 x - 8 y \text { on the region bounded }$

Multiple Choice

Find the absolute extrema of $f ( x , y ) = 4 x ^ { 2 } + 8 x y - 48 x - 8 y \text { on the region bounded }$ by the square with vertices $( 0,0 ) , ( 7,0 ) , ( 0,7 )$ , and $( 7,7 )$ .

A) absolute minimum: $( 0,7 , - 56 )$
absolute maximum: $( 0,0,0 )$

B) absolute minimum: $( 0,7 , - 56 )$
absolute maximum: $( 7,7,196 )$

C) absolute minimum: $( 1,5 , - 44 )$
absolute maximum: $( 0,0,0 )$

D) absolute minimum: $( 6,0 , - 144 )$
absolute maximum: $( 7,7,196 )$

E) absolute minimum: $( 6,0 , - 144 )$
absolute maximum: $( 0,0,0 )$